Claiming that you have a huge budget isn't a good negociation strategy. Ask Barcelona what happened once everyone knew their pockets were filled with Neymar's cash.
It has nothing to do with getting players cheap, it's because they target different profiles. KdB failed once in the PL before the got him, Rodri wasn't a very popular player etc. For sure, if you buy Sancho, a pretty popular prospect, Pogba who's crushing it in Italy, or this kind of players, the price tag is going to be very different.
Still, City spent 76M€ for KdB, 68M for Mahrez, 65M for Laporte, 63 for Rodri, there's nothing cheap there.